Empirical modeling of fresh and hardened properties of self-compacting concretes by genetic programming
Introduction
Since its development in the late 1980s in Japan, Self-Compacting Concrete (SCC) has brought a new insight into the concrete technology so that SCC has been considered as a quite revolution in the construction industry. Its introduction represents a major technological advance which leads to a better quality of concrete, increased productivity and much improved working environment on site [1]. SCC is characterized by the high fluidity under its own weight such that it can be placed without vibration, easily fill small interstices of formwork and be pumped through long distances [2].
The common practice to produce self-compacting concrete is to limit the coarse aggregate content associated with its maximum size and to use the lower water-binder ratio together with appropriate superplasticizer [3]. In order to achieve a SCC of high fluidity and to prevent the segregation and bleeding during transportation and placing, the formulators have employed a high Portland cement content and used superplasticizer and viscosity modifying additives [4], [5], [6], [7]. However, the cost of such concretes remarkably increased associated with the use of high volume of portland cement and chemical admixtures. In some cases the savings in labor cost might offset the increased cost. But the use of mineral admixtures such as fly ash, blast furnace slag and/or limestone filler etc. reduced the material cost of the SCCs and also improved fresh and hardened properties of the concretes [8], [9].
A number of studies [10], [11], [12], [13], [14], [15], [16] have been reported in the literature concerning the use of mineral additives to enhance the self-compactibility characteristics and to reduce the material cost of the SCCs. It is obviously known that use of fly ash and granulated blast furnace slag decreases the V-funnel flow time, compressive strength and ultrasonic pulse velocity but they increase the slump flow diameter and electrical resistivity of self-compacting concretes. Silica fume, however, fairy increased the V-funnel flow time, compressive strength, ultrasonic pulse velocity and electrical resistivity but caused a reduction in the slump flow diameter of self-compacting concretes.
Influence of using mineral admixtures on the fresh and hardened properties is well known in the literature. However, there exist no explicit formulations for estimating the properties of self-compacting concretes especially with mineral additives. For this purpose, empirical formulations were proposed by applying the genetic programming on the experimental dataset for prediction of slump flow diameter, V-funnel flow time, compressive strength, ultrasonic pulse velocity and electrical resistivity of self-compacting concretes containing mineral admixtures.
Section snippets
Materials
An ASTM Type I Portland cement (PC) was used to produce the various SCC mixtures. In addition, a class F fly ash (FA), a ground granulated blast furnace slag (GBS), and a silica fume (SF) were used as mineral admixtures. Table 1 summarizes physical properties and chemical composition of the cement and mineral admixtures used. The coarse aggregate used was river gravel with a nominal maximum size of 16 mm. As fine aggregate, a mixture of natural river sand and crushed limestone was used with a
Genetic programming
Genetic programming was proposed by Koza [20] to automatically extract intelligible relationships in a system and has been used in many applications such as symbolic regression [21], [22] and classification [23], [24]. A schematically overview of genetic programming is given in Fig. 1. Koza [20] explains the flowchart of GP in four main steps:
- 1.
Generate an initial population of random compositions of the functions and terminals of the problem (computer programs).
- 2.
Execute each program in the
Application of genetic programming (GEP)
The database built in the experimental part was used for the modeling of the fresh and hardened properties of SCCs. The major task herein is to define the hidden function connecting the input variables (X1, X2, X3, … , X9) and outputs (Y1, Y2, Y3, Y4 and Y5). The expected empirical models may be written in the form of following equation:The functions obtained by GEP will be used for estimating the characteristic of SCCs in the fresh state in terms of slump and V-funnel flows and
Performance of empirical models
Predicted values achieved through the proposed GEP formulations are compared with the experimental results for the slump flow diameter, V-funnel flow time, compressive strength, electrical resistivity and ultrasonic pulse velocity in Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, respectively. It was observed in Fig. 3a that the proposed GEP formulation for slump flow diameter of SCCs is able to closely follow trend seen in the experimental data within both train and test sets. Fig. 4a and b shows the
Conclusions
This paper presents a new and efficient approach for the developing empirical formulations of slump flow diameter, V-funnel flow time, compressive strength, ultrasonic pulse velocity and electrical resistivity properties of self-compacting concretes including mineral admixtures. Based on the findings of this study the following conclusion may be drawn:
- 1.
The highest correlation coefficient of 0.98 was achieved for electrical resistivity while the V-funnel flow time had the lowest R of 0.89.
- 2.
It was
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